There are two prime discount months: July and December. The intense summer heat depresses visitation in July and room rates (and airfares) plummet as temperatures soar; and people tend to travel during the holidays, not right before or after.
But the absolutely least expensive time is the week or so before Christmas. There’s a five- to ten-day stretch (it varies from year to year, depending on the calendar) between the big National Finals Rodeo convocation and the Christmas rush, during which the casinos practically give away their rooms, discounts and deals abound, and crowds are thin. (Even traffic on the Strip is light.)
As soon as Christmas Eve rolls around, however, the crowds descend and costs skyrocket. The week-long party culminates on New Year’s Eve, Las Vegas’ busiest night of the year.
The Consumer Electronics Show (CES), one of the largest conventions in the world, hits town the second week in January, then the place settles down for a bit in a post-New Years (and CES) lull.
Note that a number of Las Vegas shows are dark during this period and that few, if any, special events are taking place. But if you simply want the best values, shortest lines, easiest bookings, and potentially better weather than the rest of the country, plan your trip for this period.